I know when a certain person is trying to talk to/get in touch with me. My intuition never fails with him. What this means, I don't know. I've also had this with other people. It's kind of like...emotional telepathy? I believe it's actually a form of being what some believers in this phenomenon call being an "empath"...I believe telepathy might involve actual thoughts, and clairvoyance foresight of events, and I have neither of those. But boy do I have this intuitive empathetic connection with some people, boy howdy. I have since I was a teenager, maybe sooner. My mother swears I talked about holding hands with my dead grandmother when I was five or six.
As for "just knowing" what is the right thing to do for your self, in your own life, following "the voice within" ...does that count as intuition? I thought I might be ISFP for a while...that this "voice within" was Fi/Ni and I was confusing my Se with Ne...but then it was carefully explained to me the difference between Se and Si, and now I understand that I definitely have Ne and Si...I'm definitely an NFP, though some might debate on E or I.
I'm not sure any of these things have to do with functions, anyway. I think Ne/Ni have to do with a preference toward theory and abstract and being in your head, it's a style of thinking, and has nothing to do with other kinds of intuition.
The "just knowing" what is right for you, though....could be Fi or Ni, maybe, because that's an internal knowledge about one's self.
I'm not sure about what you're talking about in the OP, about knowing someone else's feelings for you ...I think that could be hit or miss, depending on the situation and how well you know the person. Sometimes it could be wishful thinking, and in other cases it very well be intuitively or empathetically following their patterns of behavior, and body language, etc. Sometimes you *can* tell how someone feels because their actions speak louder than words...it's apparently a gift NFs are supposed to have, anyway. It has to do with connecting patterns of behavior, though, which could be function-related and not "psychic" at all.